2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental frequency wo and the Fourier coefficients Cn such that x (1) -Σ-ο Ceinwot,
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- Consider a function a(t) with a period T, = 3 and Coz = 5 Given another function: y(t) = -2x(t+ 2) + 1 Find the Fourier coefficient Cy in terms of the Fourier coefficient C: Select one: O Cry = Crek8a/3 O Cy = Cjk4n/3 O Cky Chze jkAn/3 O CkySuppose that f(t) is periodic with period [-n, n) and has the following complex Fourier coefficients: Co = -3, 1 = -3+3i, C2 = 3, C3 = -4 + 2i, ... ... (A) Compute the following complex Fourier coefficients. C3 = (B) Compute the real Fourier coefficients. (Remember that et kt = cos(kt) + i sin(kt).) %3| ao = > a2 = > az = bi bz = %3D (C) Compute the complex Fourier coefficients of the following. (1) The derivative f (t). Co (ii) The shifted function f(t +) Co C2 Ca= (iii) The function f(3t). Co C1 = %3D2) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure 2. x(t) cos at Şekil 2
- please label the question and answer clearly. also please answer part D and E. thank you!!!4. 225Find the cosine Fourier coefficients for the function f(x) = 35 cos(3x), on 0Sxs. O A None of these. 140 and an- 35 (-1)+1 (-1)" 2n+3 2n-3 O B.40 =- 37 n=1,2,3,... 140 and an- 70 (-1)+1 (-1)" 2n +3 Oca0 =- 2n-3 n=1,2,3,... 140 and an= 元 70 (-1)*1 2n +3 (-1)" 2n-3 O Da0 =- n = 1,2,3,... %3D 70 (-1)+1 (-1)" 2n-3 2n+3 n= 0,1,2,3,... OE an=
- 2. Determine the complex Fourier coefficients co and c„ of the function simulating the periodic heating of a room if it is given that f(t) = e' – 1, 0Suppose that f(t) is periodic with period [-T, 7) and has the following complex Fourier coefficients: -4, C1 —3+ 41, С2 —D —1- 21, C3 2. (A) Compute the following complex Fourier coefficients. C_3 = 2 C_2 =-1+2i C_1 = (B) Compute the real Fourier coefficients. (Remember that ei kt cos(kt) + i sin(kt).) ao = a1 = -6 , a2 = -2 , az = 4 b, = b2 = b3 = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f' (t). Co = C1 = -4-31 C2 = C3 = (ii) The shifted function f(t + Co = C = C2 = C3 = (iii) The function f(3t). Co = C = C2 = C3 =(b) Determine the Z-transforms of the following expressions (ii) (cos 0 + i sin 0)"Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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